Conference Theme. The concept of infinity has fascinated
philosophers and mathematicians
for many centuries: e.g., the distinction between the potential and actual
infinite appears in Aristotle's Physics (in his treatment of the paradoxes
of Zeno) and the notion was implied in the attempts to sharpen the method
of approximation (starting as early as Archimedes and running through the
middle ages and into the nineteenth century). Modern mathematics opened
the doors to the wealth of the realm of the infinities by means of the
set-theoretic foundations of mathematics.

Any philosophical interaction with concepts of infinite must have at
least two aspects: first, an inclusive examination of the various branches
and applications, across the various periods; but second, it must proceed
in the critical light of mathematical results, including results from
meta-mathematics.

The conference History & Philosophy of Infinity will emphasize
philosophical,
empirical and historical approaches. In the following, we give brief
descriptions of these approaches with a number of questions that we
consider
relevant for the conference:

In the philosophical approach, we shall link questions about the
concept of infinity to other parts of the philosophical discourse,
such
as ontology and epistemology and other important aspects of philosophy
of mathematics. Which types of infinity exist? What does it mean to
make such a statement? How do we reason about infinite entities? How
do
the mathematical developments shed light on the philosophical issues
and how do the philosophical issues influence the mathematical
developments?

Various empirical sciences deal with the way we as finite human
beings
access mathematical objects or concepts. Research from mathematics
education, sociology of mathematics and cognitive science is highly
relevant here. How do we represent infinite objects by finite means?
How are infinite objects represented in the human mind? How much is
our
interaction with infinite concepts formed by the research community?
How do we teach the manipulation of infinite objects or processes?

Infinity was an important concept in philosophy and theology from the
ancient Greeks through the middle ages into the modern period. How did
the concepts of infinity evolve? How did questions get sharpened and
certain aspects got distinguished in the philosophical debate? Did
important aspects get lost along the way?

Submission. We are cordially inviting all researchers to submit
proposals for presentations covering either historical or philosophical
aspects of infinity, or dealing with empirical investigations of infinity
in relation to the historical and philosophical aspects. For more
information about submission, please consult our website at
http://www.math.uni-hamburg.de/home/loewe/HiPhI/submission.html.

FotFS VIII is sponsored by the ESF network INFTY: New frontiers of
infinity and Division for Logic, Methodology and Philosophy of
Science of the International Union for History and Philosophy of
Science (DLMPS/IUHPS).